Bejeweled, Candy Crush and other match-three games are (NP-)hard

@article{Gual2014BejeweledCC,
  title={Bejeweled, Candy Crush and other match-three games are (NP-)hard},
  author={Luciano Gual{\`a} and Stefano Leucci and Emanuele Natale},
  journal={2014 IEEE Conference on Computational Intelligence and Games},
  year={2014},
  pages={1-8}
}
The twenty-first century has seen the rise of a new type of video games targeted at a mass audience of “casual” gamers. Many of these games require the player to swap items in order to form matches of three and are collectively known as tile-matching match-three games. Among these, the most influential one is arguably Bejeweled in which the matched items (gems) pop and the above gems fall in their place. Bejeweled has been ported to many different platforms and influenced an incredible number… 
The Computational Complexity of Angry Birds
Hanabi is NP-hard, even for cheaters who look at their cards
On the Complexity of Slide-and-Merge Games
TLDR
This work defines a number of natural decision problems on a suitable generalization of these games and proves NP-hardness for 2048 by reducing from 3SAT and discusses the adaptation of the reduction to Threes.
Trainyard is NP-Hard
Cooperating in Video Games? Impossible! Undecidability of Team Multiplayer Games
We show the undecidability of whether a team has a forced win in a number of well known video games including: Team Fortress 2, Super Smash Brothers: Brawl, and Mario Kart.To do so, we give a
On the Complexity of Two Dots for Narrow Boards and Few Colors
TLDR
It is shown that Two Dots is hard even for instances involving only 3 colors or 2 columns, and it is proved that the problem can be solved in polynomial-time on single-column instances with a constant number of goals.
On the PSPACE-completeness of Peg Duotaire and other Peg-Jumping Games
TLDR
Peg Duotaire has been studied from a combinatorial point of view and two versions of the game have been considered, namely the single and the multi-hop variant, which it is proved that both versions are PSPACE-complete.
Computational Complexity of Buttons & Scissors
Buttons & Scissors is a popular single-player puzzle game by KyWorks. The level is played on an n-by-n grid, where each position is empty or has a single coloured button sewn onto it. The player’s
Tracks from hell - when finding a proof may be easier than checking it
TLDR
This paper proves that the verification problem of checking whether a candidate solution solves the level is PSPACE-complete, thus implying that Trainyard players might not only have a hard time finding solutions to a given level, but they might even be unable to efficiently recognize them.
...
1
2
3
...

References

SHOWING 1-10 OF 13 REFERENCES
Computational Complexity of Two-Dimensional Platform Games
We analyze the computational complexity of various two-dimensional platform games. We state and prove several meta-theorems that identify a class of these games for which the set of solvable levels
Tetris is Hard, Even to Approximate
TLDR
It is proved that in the offline version of Tetris, it is NP-complete to maximize the number of cleared rows, maximize theNumber of tetrises (quadruples of rows simultaneously filled and cleared), minimize the maximum height of an occupied square, or maximize thenumber of pieces placed before the game ends.
Tetris is hard, even to approximate
TLDR
It is proved that in the offline version of Tetris, it is -complete to maximize the number of cleared rows, maximize theNumber of tetrises (quadruples of rows simultaneously filled and cleared), minimize the maximum height of an occupied square, or maximize thenumber of pieces placed before the game ends.
Games, puzzles and computation
TLDR
This thesis develops the idea of game as computation to a greater degree than has been done previously, and presents a general family of games, called Constraint Logic, which is both mathematically simple and ideally suited for reductions to many actual board games.
Gaming Is a Hard Job, but Someone Has to Do It!
  • G. Viglietta
  • Mathematics, Computer Science
    Theory of Computing Systems
  • 2013
TLDR
Several video games published between 1980 and 1998 are studied, including Pac-Man, Tron, Lode Runner, Boulder Dash, Pipe Mania, Skweek, Prince of Persia, Lemmings, and Starcraft, to establish some general schemes relating the computational complexity of a video game to the presence of certain common elements or mechanics.
A Survey of NP-Complete Puzzles
TLDR
This article surveys NP-Complete puzzles in the hope of motivating further research in this fascinating area, particularly for those puzzles which have received little scientific attention to date.
A Casual Revolution: Reinventing Video Games and Their Players
The enormous popularity of the Nintendo Wii, Guitar Hero, and smaller games like Bejeweled or Zuma has turned the stereotype of the obsessed young male gamer on its head. Players of these casual
Casual games discussion
TLDR
This article will analyse the ongoing discussion on casual games by providing clarification of the different meanings of casual and a framework for an overall understanding of casual in the level of expanded game experience.
Candy Crush is NP-hard
  • T. Walsh
  • Computer Science, Mathematics
    ArXiv
  • 2014
We prove that playing Candy Crush to achieve a given score in a fixed number of swaps is NP-hard.
Computers and intractability, volume 174
  • freeman San Francisco,
  • 1979
...
1
2
...